WASHINGTON (Reuters) - A leading U.S. House of Representatives member has privately urged banks to push Senate Democrats to agree to further easing of financial rules in a bid to end a stalemate over the first rewrite of regulations since the 2007-2009 financial crisis, sources said on Tuesday.

Representative Jeb Hensarling, who is leading House discussions on the first rewrite of the 2010 Dodd-Frank reform law, made his case to industry lobbyists at a private meeting on Monday, three people with direct knowledge of the meeting told Reuters.

Hensarling's strategy will likely increase pressure on moderate Democrats in the Senate, which is in a standoff with the House over the bipartisan legislation to ease rules on small lenders. The Senate passed the bill last week.

Those Democrats, who helped write and pass the Senate bill, have said they will walk away if the House pushes for further rule easing. But Hensarling, who chairs the House Financial Services Committee, has been adamant that the lower chamber will not rubber-stamp the Senate version.

At the meeting on Capitol Hill, Hensarling asked bank lobbyists, who are anxious to see the bill signed into law, to persuade Senate Democrats to consider the House's changes, the sources said.

Hensarling has identified 30 House bills he would like to add to the Senate text, but some lawmakers and lobbyists are concerned doing so could upend a delicate balance in the Senate, where Democratic and Republican support is required to pass legislation.

Hensarling says the changes he is seeking are moderate and have significant support from House lawmakers in both parties.

"Chairman Hensarling is not fighting for himself; he’s fighting on behalf of the whole House – including the Democrat sponsors, cosponsors, and supporters of these strong, bipartisan bills," said Sarah Flaim, Hensarling's spokeswoman in a statement.

Given tensions among Democrats, Hensarling's strategy could give the bill's critics ammunition. Prominent Democratic progressives, including Senator Elizabeth Warren, have accused Democratic backers of the bill in the Senate of giving handouts to big banks and putting consumers at risk.

"House Republicans & bank lobbyists want the bill to roll back more consumer protections and include more big bank giveaways. Senate supporters of this bill must not let a bad bill get even more dangerous," Warren tweeted on Wednesday in response to Reuters' report.

Congress passed the Dodd-Frank law after the 2008 crisis to ensure banks are sufficiently capitalized to weather a future downturn, and to discourage them from taking on excessive risk. But critics of the law say it has discouraged lending, particularly among small banks, through excessive regulations.

The Democratic backers, including Senator Heidi Heitkamp, have urged the House to not change the bill, but have been silent on the specific changes Hensarling seeks.

"I respect that some House Republicans want to amend our legislation, but doing so would unfortunately prevent Congress from achieving the shared goal of providing relief for community banks and credit unions so they can serve communities across rural America," Heitkamp said in a statement.